Games of social distancing during an epidemic: Local vs statistical information

The choices of a population to apply social distancing are modeled as a Nash game, where the agents determine their social interactions. The interconnections among the agents are modeled by a network. The main contribution of this work is the study of an agent-based epidemic model coupled with a social distancing game, which are both determined by the networked structure of human interconnections. The information available to the agents plays a crucial role. We examine the case that the agents know exactly the health states of their neighbors and the case they have only statistical information for the global prevalence of the epidemic. The agents are considered to be myopic, and thus, the Nash equilibria of static games for each day are studied. Through theoretical analysis, we characterize these Nash equilibria and we propose algorithms to compute them. Interestingly, in the case of statistical information the equilibrium strategies for an agent, at each day, are either full isolation or no social distancing at all. Through experimental studies, we observe that in the case of local information, the agents can significantly affect the prevalence of the epidemic with low social distancing, while in the other case, they can also affect the prevalence of the epidemic, but they have to pay the burden of not being well informed by applying strict social distancing. Moreover, the effects of the network structure, the virus transmissibility, the number of vulnerable agents, the health care system capacity and the information quality (fake news) are discussed and relevant simulations are provided.